Jones informed the writers of the General Dictionary that Newton "ascertained the law of the motion in an ellipse, "when the force was inversely as the squares of the distance, 'during the winter between 1676 and 1677, and that, having "resumed the consideration of it in 1683, he then added some "other propositions concerning the motion of the heavenly "bodies." It is just possible that Jones was thinking of Newton's conversation in 1677 with Donne and Wren, but certainly the allusion to the year 1683 is wrong, and we may safely assert that the time mentioned for the discovery of the law of the motion in an ellipse under gravitation is also inaccurate. 25 CHAPTER IV. INVESTIGATIONS IN 1684. NEWTON never showed an undue haste in publishing his discoveries, though he was willing enough to communicate them to his friends if directly asked. Hence the results of his investigations in 1679, like those in 1666, were not for some. years sent to any Society, and the scientific world remained unaware of their extent and value. In January, 1684, Halley*, "from the considerations of the sesquialter proportion of Kepler, concluded that the centripetal force decreased in the proportion of the squares of the "distances reciprocally"; but was unable to deduce from that hypothesis the motion of the heavenly bodies. In the same month he went to London, where he met Wren and Hooke. He found that Wren had come to the same opinion as himself, but equally was unable to find the consequences thereof. Hooke, however, boasted "that upon "that principle all the laws of the celestial motions were to be demonstrated, and that he himself had done it." But nothing could be extracted from Hooke, and, though at last he promised to show his demonstration to Wren, he revealed nothing; and there can be no doubt that Wren and Halley considered that his boast was not justified by the facts. On this, in August, 1684, Halley went to Cambridge, and mentioned the problem to Newton, and "then learned the * Halley's letter of June 29, 1686, printed below, p. 162. good news that" Newton "had brought this demonstration "to perfection," of which demonstration he promised to send a copy to Halley. Newton could not, however, lay his hands on the original paper, and so, "not finding it, did it again, and "reduced it into the propositions"* which he sent to Halley by Paget in November, 1684. The account given by Conduitt is substantially the same†. After mentioning the inability of Halley, Wren, and Hooke to find the orbit described under a central force which varied inversely as the square of the distance, he says that Halley set out for Cambridge in May (which obviously is a slip for August), 1684, to consult Newton. "Without mentioning "either his own speculations, or those of Hooke and Wren, he at once indicated the object of his visit by asking Newton "what would be the curve described by the planets on the "supposition that gravity diminished at the square of the "distance. Newton immediately answered, an Ellipse. Struck "with joy and amazement, Halley asked him how he knew it? Why, replied he, I have calculated it; and being asked for "the calculation, he could not find it, but promised to send it "to him. After Halley left Cambridge, Newton endeavoured "to reproduce the calculation, but did not succeed in obtaining "the same result. Upon examining carefully his diagram and "calculation, he found that in describing an ellipse coarsely 'with his own hand, he had drawn the two axes of the curve “instead of two conjugate diameters somewhat inclined to one 'another. When this mistake was corrected he obtained the "result which he had announced to Halley." The propositions were not sent to Halley until November, 1684, and presumably were on the conservation of areas under a central force, the law of force in a focus under which an ellipse can be described, and the converse on the orbit described by a particle under a central force which varies inversely as * Newton's letter of July 14, 1686, printed below, p. 165. the square of the distance (Principia, book i. props. 1, 11, and cor. 1 of prop. 13). It is possible that they also included the law of force to the centre under which a circle is described, and the law of force to any point under which any curve is described (book i. props. 4, 6). Fortunately, Newton, after Halley's visit in August, did not confine himself to writing out his old demonstrations, but continued his investigations, though doubtless he had no idea of the extent to which they could be pushed, or how far they were likely to lead him. By the Michaelmas Term, 1684, he had put them together in manuscript in a connected form, and this manuscript he read as his professorial lectures in that term. Newton had been appointed Lucasian professor on Oct. 29, 1669, and under the statutes relating to the chair it was his duty to lecture for one hour at least once a week during term, and to be accessible to students during two hours on two days in every week in term, and on one day in every week in vacation if he were in residence; but it seems to have been universally understood that the duty of lecturing was confined to one term in the year, and his amanuensis states that the lectures usually lasted only half an hour. It is most likely that the lectures were read or dictated as rapidly as they could be taken down, and that any explanations, were given in interviews in his rooms. in the week following the lecture. All junior sophs and all bachelors of arts under the standing of master were required to attend, but the rule was not enforced. Newton's lectures for eighteen out of the first nineteen years of his tenure of the chair are extant*; except in the session *They are in four manuscript volumes preserved in the University Library, containing respectively the lectures from 1669 to 1672, those from 1673 to 1683, those for 1684 and 1685, and those for 1687. The lectures from 1669 to 1672 are not holograph, but the marginal notes and corrections are in Newton's handwriting; they were deposited in the Library in 1674. The rest are probably holograph. The volumes 1669–70, they were always given in the Michaelmas Term. He seems never to have repeated his lectures, and, roughly speaking, the lectures of one October continue from the point at which those in the preceding December terminated. The lectures from 1669 to 1672 were on optics, those from 1673 to 1683 on arithmetic and algebra, those in 1684 and 1685 comprised some of the propositions afterwards printed in the Principia; those in 1686 are missing; and those in 1687 were a popular exposition of the third book of the Principia. The lectures given in the Michaelmas Term, 1684, were nine in number, and are entitled De Motu Corporum. The manuscript of them may be taken as being a rough draft of the beginning of the first book of the Principia, to which the numbers of the propositions given below refer. The first lecture is on the definitions as given in the Principia; the second on the laws of motion; the third on the laws of motion and the first four lemmas; the fourth on the remaining seven lemmas in section i; the fifth on props. 1-9, lemma 12, and prop. 10; the sixth on props. 11, 12, lemmas 13, 14, and props. 13–15; the seventh on props. 16-19; the eighth on lemma 16, and containing the lectures for 1684, 1685, and 1687, have George I.'s bookplate (Bishop Moore's library) in them, and this seems to indicate that they were not deposited in the Library till 1715; but probably the plate has been pasted in by error, for Cotes, writing to Jones on Sept. 30, 1711, says: "We have nothing of Sr Isaac's that I know of "in Manuscript at Cambridge besides the first draught of his Principia as he read it in his Lectures, his Algebra Lectures which are printed, "and his Optick Lectures the substance of which is for ye most part "contained in his printed Book but with further Improvements; " and there appear to be no other manuscripts save the volumes for 1684-5 and 1687 to which Cotes's remark about the first draft of the Principia can refer. Only five of the lectures for 1687 are written out in Newton's manuscript; these are divided into 28 sections. There is also another copy of them in the Library of Trinity College, written by Cotes in 1700 when he was an undergraduate, and contained in a note-book wherein he has also copied the (then unpublished) lectures of 1673-1683. See the Cotes Correspondence, pp. lv, xci-xcviii, 209. |